Six axis machine tool

ABSTRACT

A machine such as a machine tool includes a pair of spaced platforms. One platform (11, 31, 185, 72, 159, 142) may mount an operator such as a tool in a spindle and the other platforms (10, 20, 180, 170, 144, 163) may mount an object such as a workpiece. The spaced platforms are joined by six powered and extensible legs (20-25, 40-45, 64-69, 145-150, 166, 182-84, 187-89) joined to the respective platforms by universal joints. The length of the legs is individually manipulated to vary the position of the platforms and, therefore, the object and operator relative to each other in six axes. The powered legs may be hydraulic cylinders (20-25) or recirculating ball screw driven (195, 197, 198). The distance between the spaced platforms may be measured by separate extensible instrument arms (130, 131, 171) which join the platforms. The instrument arms may use a digital position device (238, 240) to measure the extension and contraction of the instrument arms or may use a laser interferometer (267) for that purpose. The changes in the length of the instrument arms may be used to generate signals that control the extension and contraction of the powered legs. A method is also disclosed for converting part program coordinate block instructions into instructions for varying the length of the powered legs.

BACKGROUND OF THE INVENTION

This invention relates to a machine for locating an operator withrespect to an object, and more particularly to a versatile machine toolin which the tool can be moved in three lineal directions and threerotational directions in relation to the surface of a workpiece.

The most versatile form of cutting tool type machine tool presently inuse is the so-called machining center which typically can accomplishmilling, drilling, boring and tapping operations in up to five axes ofmovement, the three linear orthagonal axes and two rotationaldirections. Since its introduction over thirty years ago, the machiningcenter's basic components have not changed. They typically include abed, an upright column and a spindle head carried by the column. Arotary table for holding a workpiece is typically mounted on the bed andprovides one of the rotary directions of motion. The column and tablemove relative to each other for one of the linear directions of motion,the spindle head and table move relative to each other in a verticaldirection for a second linear axis of motion, and the spindle head andworkpiece move horizontally with respect to each other for the thirdlinear direction of motion. The fifth axis is provided by rotating thespindle head or the work table in a vertical plane relative to eachother.

A sixth axis of rotary motion is available in the present machiningcenters by controlling the angular position of the spindle. The presentmachining centers may have either a horizontal spindle or a verticalspindle and they typically are controlled by computer numerical control.The machining centers usually have mechanisms for automatically changingtools from and to a magazine of tools associated with the machiningcenter, and will often have automatic workpiece handling as well.

To achieve the full six axes of motions in a present machining centerrequires that the movements of the table, column, spindle head, spindle,and bed be coordinated and that these sometimes massive components bemoved in very controllable finite increments. Because all of thesecomponents are being moved, many times simultaneously under computernumerical control, accuracy requires a rigidity to the components and anaccurate path through which the components can be moved. This hasresulted in the development of more rigid and massive components such asfor the bed and column and very expensive and finely formed ways alongwhich the components can travel relative to each other in the lineardirections.

Although the modern machining center provides very accurate machining,the machining center becomes very complex and expensive when it isdesigned to provide the maximum versatility of being able to machine anypoint on the exposed five surfaces of the typical cubic workpiece.

SUMMARY OF THE INVENTION

Instead of being constrained by the typical construction of machinetools as exemplified by the modern machining center, our inventionfocuses on the ultimate task of bringing a tool to bear against aworkpiece. To accomplish this task with the greatest degree offlexibility, our invention has the effect of suspending the spindle inair relative to the workpiece on a plurality of leg-like members thatare connected between a support for the workpiece and a support for thespindle. The leg members can be manipulated by a plurality of actuatorsto position the spindle. The tool being held by the spindle can therebybe brought to bear against any exposed surface of the workpiece becausethe spindle can be moved through space in three orthagonal lineardirections and in three rotational directions about each of the linearaxes. Furthermore, all six degrees of freedom of motion are activelycontrollable in our unique arrangement. This contrasts with the typicalmachine tool in which several moving parts each have six degrees offreedom of motion and most are not actively controlled. Also unlike thetypical machine tool, the sixth axis in our arrangement allows angularorientation of the tool or other operator. An example would be theangular orientation of a multiple tool head in a spindle.

Although our invention finds particular use in machine tools, it isuseful for locating other types of operators relative to an object andcan be used with multiple forms of tools other than the typical rotarycutting tools. It can also be used to simply position two platformsrelative to each other.

In summary, in the broadest sense our invention relates to a machine forlocating an operator relative to an object which comprises supports forthe operator and object that are spaced from each other, six leg memberswith each leg member being joined at spaced points along the leg memberto the two supports, the areas circumscribed by the junctions of the legmembers in the two supports being substantially the same, together withmeans for individually manipulating at least certain of the leg membersto vary the position of the points of such leg members relative to eachother, and to thereby alter the position of the operator with respect tothe object.

Also in the broadest sense, our invention relates to a machine tool forlocating a tool relative to a workpiece in which the tool is locatedrelative to a first support, the workpiece is located relative to asecond support, the two supports are connected by six legs with meansfor manipulating the legs to vary the lengths of the legs.

Preferably, the machine also includes means for sensing the changes inposition of the points of the leg members, and control means responsiveto the sensing means, for coordinating the manipulating means.

In the preferred embodiments, the junctions of the six legs to the twosupports generally define edges of a regular octahedron or the junctionsof the leg members to the supports define the corners of a six-sidedpolyhedron in each support.

In the preferred embodiments, the leg members are six linearlyextensible legs and the manipulating means includes an actuator for eachleg for individually extending and contracting the length of the leg.The six leg members are arranged in pairs and the leg members of eachpair are at an angle relative to each other. The sensing means may beformed as part of a plurality of instrument arms. The instrument armsare joined between the supports in a known relationship to the legmember so that a change in position of the points on the leg members istranslated into a changes in length of the instrument arm.

Our invention also relates to preferred forms of extensible powered legsand instrument arms that find use in the machines and mechanisms of theinvention but which may also be usable for other purposes.

In the preferred embodiments, one of the supports, such as the supportmounting a workpiece, may be mounted on the floor as a base while theother support is held above the base by the six legs. Furthermore, thebase may include columns that mount the ends of three legs disposedgenerally in the plane of the upper support while three more legs extendbetween the base and the upper support. Alternatively, the upper supportmay be stationary, such as supported on columns rising from a floor,while the second support is suspended beneath it on the six legs.

Our invention also comprises a method of locating an operator, such as atool, relative to an object, such as a workpiece, by locating theoperator relative to a first support and locating the object relative toa second support, connecting the supports together by six extensiblelegs, and manipulating the length of the legs to provide up to threelinear degrees of motion and three rotational degrees of motion, or anycombination thereof, to the tool relative to the workpiece.

Our invention also relates to a method of converting standard partprogram machine coordinate instructions into instructions that relatesolely to changes in the length of the legs. The method involvesconverting initial and final positions of the ends of the legs intovectors which are then manipulated to determine changes in the length ofthe leg and which may also be used to determine changes in the rate ofchange of the length of the legs.

The tool or other operator may be a rotating cutting tool, a wire saw, anozzle for an oxyacetylene or plasma torch, a laser beam, an electricdischarge wire, a probe or other measuring device, a drafting pen,sewing or knitting needles, grips, and so forth without limitation. Thetool or other operator may be held stationary while the workpiece orother object is moved, or vice versa.

It is a principal object of this invention to provide a machine forbringing an operator, such as a tool, into contact with an object, suchas a workpiece, with the maximum degree of freedom of motion of theoperator with respect to the object.

It is a further object of this invention to provide a novel machine toolstructure for supporting a tool relative to a workpiece while providingsix degrees of freedom of motion of the tool with respect to theworkpiece.

It is another object of the invention to provide a machine tool havingsix degrees of freedom of motion with each degree of motion under activecontrol.

It is also an object of the invention to provide a machine for bringingan operator into contact with an object in which the position of theoperator relative to the object is sensed independently of themechanisms for moving the operator relative to the object.

It is yet another object of the invention to provide a machine which isstructurally stiff and operationally stable while providing maximumdegrees of motion of an operator relative to an object.

The foregoing and other objects and advantages of the invention willappear in the detailed description that follows. In the description,reference is made to the drawings which illustrate several preferredembodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view in elevation of a machine tool in accordance with theinvention;

FIG. 2 is a top plan view of the machine tool of FIG. 1;

FIG. 3 is a view in perspective of a second embodiment of a machine toolin accordance with the present invention;

FIG. 4 is a view in elevation of the machine tool of FIG. 3;

FIG. 5 is a top view of the machine tool of FIGS. 3 and 4 as viewedthrough the section of the plane 5--5 of FIG. 4;

FIG. 6 is a view in elevation of a third embodiment of a machine tool inaccordance with the invention;

FIG. 7 is a partial view in elevation of a leg and instrument armarrangement usable with any of the embodiments;

FIG. 8 is a schematic view of a control for a machine tool in accordancewith the invention;

FIG. 9 is a schematic diagram of a second embodiment of a control;

FIG. 10 is a schematic diagram of a third embodiment of a control;

FIG. 11 is a view in perspective of a fourth embodiment of a machinetool in accordance with the invention;

FIG. 12 is a view in perspective of a fifth embodiment of a machine toolin accordance with the invention;

FIG. 13 is a view in perspective of a sixth embodiment of a machine toolin accordance with the invention;

FIG. 14 is a view in longitudinal section of a powered extensible legusable with the machine tools;

FIG. 15 is a partial view in longitudinal cross section, to an enlargedscale, of one of the yoke assemblies for connecting the powered leg to aplatform or support;

FIG. 16 is a view in longitudinal cross section through the yokeassembly of FIG. 15 and taken in the plane of the line 16--16 in FIG.14;

FIG. 17 is a view in perspective of the yoke assembly of FIGS. 15 and16;

FIG. 18 is a foreshortened view in longitudinal cross-section of aninstrument arm usable with the machine tools;

FIG. 19 is a view in section of one end of the instrument arm of FIG. 18and taken in the plane 19--19 in FIG. 18;

FIG. 20 is a schematic view of an instrument arm using a laserinterferometer for measuring distances; and

FIG. 21 is a vector diagram illustrating a method for determiningposition commands for the legs of the machine tools.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIGS. 1 and 2, the machine tool of the first embodiment hasa base 10 in the nature of a support or platform and a spindle supportor platform 11 spaced from the base 10. A spindle head 12 is mounted onthe spindle platform 11 and is adapted to receive a rotating cuttingtool 13. A spindle drive assembly indicated generally by the numeral 14is mounted on the spindle platform 11 and the drive includes a motor 15connected by a power train to the spindle head 12 in a usual manner. Thebase platform 10 carries a workpiece support 16 which in turn receives aworkpiece represented by the part 17.

The spaced platforms 10 and 11 are joined together by six powered andextensible legs 20-25. Each of the legs is pivotally mounted at itslower extremity to the base platform 10 by a ball and socket joint 26.Similarly, each of the upper ends of the legs 20-25 is pivotallyattached to the spindle platform 11 by a second ball and socket joint27.

The legs 20-25 may be formed of telescoping upper and lower parts 20aand 20b for example. The telescoping parts may be the piston rod 20a andcylinder 20b of a hydraulic cylinder. The length of such legs can beadjusted by controlling the volume of hydraulic fluid in each end ofeach cylinder.

The position of the spindle support 11 relative to the base support 10and therefore the position of the cutting tool 13 relative to theworkpiece 17 can be adjusted by simultaneously manipulating the lengthof each of the six legs 20-25. Within an envelope of motion the cuttingtool 13 can be applied against all five exposed surfaces of a cubic typeworkpiece. The only constraints to the envelope of motion relative tothe five exposed surfaces are the spread of the joints 26 on the basesupport 10 and the spread of the second joints 27 on the spindle support11, the minimum and maximum length of the legs 20-25, the total range oflinear motion of each of the legs, and the need to avoid placing certainlegs in a common plane for purposes of stability. Within the envelope ofmotion, this construction allows the machining of contours in threedimensions as well as straight line point-to-point machining.

The simultaneous manipulation of the length of each of the legs 20-25can achieve motion in all six axes. That is, motion in a lineardirection along each of the three orthagonal axes and rotary motionabout each of those three axes.

In the embodiment of FIGS. 1 and 2, the six legs may be considered to bearranged in three pairs. That is, the legs 20 and 21 constitute a pair,the legs 22 and 23 constitute a second pair, and the legs 24 and 25constitute a third pair. It should be noted that the legs of each pairare arranged so that they are at an angle with respect to each other.The joints 26 of the pair of legs 20 and 21 are close to each other. Thejoints 27 of adjacent legs 20 and 25, for example, are also close toeach other. The effect is that the lower joints 26 generally define atriangle and the upper joints 27 also generally define a triangle. Thesetwo triangles and the six legs generally define edges of an octahedron.As shown in FIGS. 1 and 2, the area of the base platform 10circumscribed by the lower ball joints 26 and the area of the spindlesupport 11 circumscribed by the upper ball joints 27 are substantiallythe same. This is advantageous for several reasons. First, such anarrangement maximizes the structural stiffness of the machine. Secondly,the footprint of the machine is minimized for a particular cubic size ofworkpiece to be handled. Also, a greater envelope of surface area forthe workpiece can be accommodated before certain legs and supports arepositioned in a common plane thereby creating a potentially ambiguousposition.

Referring to FIGS. 3-5, the second embodiment includes a base support orplatform 30, a spindle support 31 which mounts a spindle head 32 adaptedto receive a cutting tool 33. The spindle head is rotated by a spindledrive 34. The base support 30 and spindle support 31 are connected bysix extensible legs 40-45. The legs are arranged in three pairs such asthe pair 40 and 41 and legs of each pair cross each other so that theyare again mounted at an angle with respect to each other. The legs 40-45are also formed of telescoping upper and lower elements 40a and 40b, forexample.

The legs 40-45 are joined to the base support 30 at a first point neartheir lower end by a joint indicated generally by the numeral 50. Thejoint 50 includes a clevis 51 mounted for rotation about the axis of ashaft 52 that projects from the base support 30. A typical trunnion 53engages the lower element 40b-45b of each leg and is rotatably mountedin a clevis 51. It will thus be seen that a joint 50 provides twodegrees of freedom of movement.

The upper telescoping portions 40a-45a of the legs are similarly joinedto the spindle support 31 at second points along the length of the legsby joints 54. The joints 54 likewise consist of a clevis 55 rotatablymounted on a shaft 56 extending downwardly from the underside of thespindle support 31 and a trunnion 57 which supports the upper legportions 40a et seq. in the clevis 55. As can be seen in FIG. 5 inparticular, the joints 50 and 54 and their attachments to the supports30 and 31 define the corners of a six-sided polygon in each of the twosupports. As is apparent from FIGS. 3-5, the area of the base support 30that is circumscribed by the connections of six lower joints 50 with thebase support 30 is substantially the same as the area of the spindlesupport 31 that is circumscribed by the connections of the six upperjoints 54 with the spindle support 31.

The shafts 52 and 56 of the joints 50 and 54 can be mounted in theirrespective supports to project in any direction. The ball joints of thefirst embodiment could also be used in this second embodiment, and thetrunnion joints of this second embodiment could be used in the first.

The base support 30 mounts a workpiece support 58 which holds aworkpiece exemplified by the part 59.

The legs 40-45 may also be formed as hydraulic cylinders with the pistonrod defining the upper end 40a et seq. and the cylinder portion formingthe lower ends 40b et seq. Because the piston rod can rotate within thecylinder, the two degrees of motion afforded at each of the joints 50and 54 are sufficient. If the upper and lower portions of the actuatorsforming the legs cannot be allowed to twist, an actuator other than ahydraulic cylinder is used to accomplish the extension, and a thirddegree of rotational motion will be required in one or the other of theupper and lower joints 50 and 54. In the leg of FIGS. 14-17, anadditional degree of motion is required in the joints or compensationmust be provided for the linear inaccuracy resulting from relativerotation of the telescoping parts introduced by slight angulardisplacement of the yoke assemblies relative to each other. Instead ofusing hydraulic cylinders as the actuators for the legs, any means forachieving linear motion can be used such as forming the upper portion ofeach leg as a lead screw and mounting a rotating nut in the lowerportion of the leg or vice versa. Alternatives are linear motors,recirculating ball screw drives, chain drives, and so forth.

In the third embodiment of FIG. 6, neither the tool nor the workpiece islocated within the envelope defined by the leg structure. The workpiece60 is mounted on a workpiece support 61 which in turn is mounted on abase 62 that is attached to an upright 63. The six legs 64-69 areconnected at one end to the upright 63 by trunnion joints 70 in a mannersimilar to that of the second embodiment. The opposite ends of the legs64-69 are connected by trunnion joints 71 to the spindle support 72. Thespindle support carries a spindle 73 adapted to mount a tool 74 and thespindle 73 is driven by a spindle drive 75. The tool 74 projects awayfrom the envelope defined by the legs 64-69. The third embodiment isotherwise the same as the first embodiment.

In the third embodiment, the workpiece support 61 may be mounted on wayssupported by the base 62 so that the workpiece support 61 with theworkpiece 60 may move relative to the tool 74. Even though the workpiece60 is not mounted on the upright 63, the workpiece location relative tothe upright support 63 can be fixed, or at least known, at any instantin time.

Other arrangements of spindle and workpiece can also be employed, suchas mounting the workpiece above the spindle or mounting an upright 63 asin the third embodiment of FIG. 6 on ways so that it can travel alongthe length of a workpiece.

The legs must be moved in a coordinated manner in order to position thesupports or platforms relative to each other. The coordinated movementis preferably accomplished by a computer control which provides aposition signal for each leg to achieve a desired position for thespindle platform relative to the base platform and therefore for thecutting tool relative to the workpiece. Suitable control schemes areillustrated in FIGS. 8 and 9. In FIG. 8, the leg in the form of ahydraulic cylinder such as the legs 20-25 are controlled by a servovalve 100 which controls the volume of hydraulic fluid in the cylinderon each side of the piston and therefore the position of the piston rodwithin the cylinder. A computer 101 produces an output position commandin the line 102. That position command is compared in a summing circuit103 with a feedback position signal in a line 104 leading from anexciter/demodulator 105 that receives the signal from a sensing head 106traveling along a magnetic scale 107. The sensing head 106 is coupled tothe piston rod 20a et seq. so that changes in position of the piston rodwill be reflected in changes in position of the sensing head 106 alongthe magnetic scale 107 which is at a known position, either fixed orvarying, with respect to the hydraulic cylinder 20b et seq. The summingcircuit 103 produces a position error signal in a line 108 which inputsto an integration network 109, the output of which is a velocity commandin a line 110. The velocity command is compared with a velocity feedbacksignal in a line 111 leading from the exciter/demodulator 105 and thetwo signals are fed to a summing circuit 112 which produces an outputsignal representative of a velocity error. This velocity error signal isfed to a compensation network 113 where phase shift compensation takesplace, and the resulting compensated signal is fed to an amplifier 114which in turn controls the servo valve 100.

A similar control loop leading from the computer would be provided foreach of the six legs 20-25 and the computer 101 would generate an outputposition command for the desired position of each of the six legs toachieve a particular finite position of the cutting tool relative to theworkpiece.

The control arrangement of FIG. 9 is similar to that of FIG. 8 but isshown in relation to a motor 120 rotating a lead screw and nutarrangement. An encoder or resolver 121 is connected to the motor 120 toprovide a position feedback signal through the exciter/demolulator 122,and that position signal is compared at a summing junction 123 with theposition command from the computer 61 to produce a position error signalfed to the integration network 124 which outputs a velocity commandcompared at a summing junction 125 with the velocity position signalfrom a tachometer 126 connected to the motor 120. A compensation network127 functions to produce an appropriate signal to an amplifier 128connected to the motor drive. Once again, there would be a similar loopfor each of the six legs of the machine.

The control schemes of FIGS. 8 and 9 employ closed loop control.However, by using a stepping motor it is not necessary to have a closedloop control. An example of a control system using a stepping motor isshown in FIG. 10.

Position signals can be provided by sensors that are directly connectedto each of the legs or to the actuators for the legs. However, a moreaccurate approach uses separate instrument arms. Such an arrangement isshown in FIG. 7.

In FIG. 7, a six legged machine tool of the embodiment shown in FIGS.3-6 has separate instrument arms 130 and 131 associated with respectivepowered legs 44 and 45, respectively. The instrument arms 130 and 131are each linearly extensible and are connected at their lower ends tothe base platform 30 by trunnion joints 132 and at their upper ends tothe spindle platform 31 by trunnion joints 133. The trunnion joints 132and 133 are the same in structure and operation as the joints 50 and 54used to connect power legs 44 and 45 to the platforms 30 and 31.

The instrument arms 130 and 131 are used solely for the purpose ofsensing the relative positions of the platforms. The instrument arms caninclude a sensing head traveling along a magnetic scale to provide thedesired feedback signal as to length and therefore as to position. Otherforms of instrument arms can also be used. The advantage in using theseparate instrument arms is that the load deflections that will occur inthe power legs and their joints will not be translated into errors inthe position of the cutting tool. The instrument arms being smaller andlighter and carrying no weight other than their own, are not subject tothe same forces and deflections to which the powered legs are subject.

Although the instrument arms 130 and 131 are shown mounted parallel withrespective power legs, it is not necessary for the instrument arms to beso mounted. Instrument arms are not required to be associated with anyparticular power leg. It is, however, necessary to have at least sixinstrument arms to provide an unambiguous set of signals for thepositions of the supports or platforms relative to each other.

In the fourth embodiment of FIG. 11, one of the platforms is elevatedand the second platform is suspended from the first platform on the sixlegs. Specifically, a support structure is formed from three uprightcolumns 140 joined together by a triangular framework of members 141. Aspindle housing 142 is supported on the triangular framework of members141 with a spindle 143 pointing downwardly towards a workpiece platform144. The workpiece platform 144 is suspended on six extensible poweredlegs 145-150 which are arranged in pairs of crossing legs, similar tothe arrangement of the legs 40-45 in the second embodiment of FIGS. 3, 4and 5. The workpiece platform 144 may mount a pallet with a workpiece(not shown) in the usual manner. The legs 145-150 are pivotally joinedat their upper ends to the members 141 and at their lower ends to theworkpiece platform 144 in a manner similar to that of the secondembodiment.

One advantage of suspending a platform on the six legs is that in caseof a gross power failure which could cause the power legs to lose theirability to support a platform, the work platform 144 would move awayfrom the spindle. This would result in no damage to either the spindle,the tool, or the workpiece because there would be no collision betweenthe parts. In contrast, in an arrangement as shown in the first andsecond embodiments, a gross power failure in which the power legs losetheir ability to support a platform could result in the spindle crashinginto the workpiece or workpiece support.

Instead of the workpiece platform being suspended beneath the spindleplatform, the workpiece platform could be above a suspended spindleplatform. Then, chips would naturally fall away from the workpiece.

The fifth embodiment of FIG. 12 also suspends a workpiece platform froma support. In addition, it provides an instrument arm associated witheach of the six power legs and a spoke-like system of connections of theends of the powered legs and instrument arms to the platform andsupport.

Specifically, the fifth embodiment of FIG. 12 has three upright columns155 joined at their base by three I-beams 156 (two of the beams areshown foreshortened for clarity). The top of each column 155 carries abearing plate 157 on which a vibration isolation member such as a coilspring 158 rests. A spindle housing 159 has three radiating support arms160 in the form of I-beams. The outer ends of the support arms 160 eachmounts a bearing plate 161 which rest upon a respective isolation member158.

The spindle head 159 is mounted on top a ring platform 162 from whichtwo series of spokes 163 and 164 project. The spokes 163 and 164 are oftwo lengths that alternate around the ring platform 162 and the spokesmount the universal joints 165 that connect the upper ends of sixpowered legs 166 to the platform 162. The lower ends of the powered legs166 are connected to universal joints 167 mounted at the ends of spokes168 and 169 which project radially from a ring-like work platform 170.The spokes 163, 164 and 168, 169 are of different lengths to accommodatethe overlapping and crossing arrangement of the powered legs 166, whichis similar to that in the second and fourth embodiments.

A similar arrangement of rings and spokes is used to mount universaljoints at the ends of six instrument arms 171. That is, a second ringstructure 172 is disposed beneath the ring support 162 at the spindleend and about the spindle 173. A series of radially projecting spokes174 and 175 of two different lengths project from the ring 172. Thebottom workpiece platform 170 contains a second ring 176 from which twoseries of spokes 177 and 178 project to mount the universal joints atthe bottom ends of the instrument arms 171. The instrument arms 171 arearranged in pairs of crossing arms in the same manner as the poweredlegs 166.

The use of spokes emanating from the platform allows the powered legsand instrument arms to be removed from close proximity to the centralaxis of the spindle head and workpiece support with the result that itis easier to load a workpiece onto the workpiece platform. This isillustrated in FIG. 12 in which a phantom line identifies a cubicworkpiece which could be accepted by the machine tool and it may benoted that there is an opening through the powered legs 166 andinstrument arms 171 to accommodate the insertion and removal of aworkpiece of that size.

The ring structure 172 and the ring 176 can be structurally independentfrom the ring platform 162 and the work platform 170, the instrumentarms 171 can be structurally isolated from the deflections of theplatforms induced by the powered legs 166.

The sixth embodiment of FIG. 13 arranges three of the six legs in adifferent attitude than that of the prior embodiments. Specifically,three of the legs are mounted in or near a common plane that includesthe upper platform. As shown in FIG. 13, a base 180 of generallytriangular shape mounts triangular columns 181 at each of its corners.Three powered legs 182, 183 and 184 extend from universal jointsdisposed near the upper end of each of the columns 181. The other endsof the three legs 182, 183 and 184 are mounted in universal joints atthe corners of a triangular spindle platform 185 which mounts a spindlehead 186. The remaining three powered legs 187, 188 and 189 extend fromuniversal joints in the base 180 upward to the three corners of thetriangular spindle platform 185. A workpiece platform 190 rests on thebase 180 within the envelope of the three lower legs 187, 188 and 189.

The embodiment of FIG. 13 functions in the same manner as the otherembodiments and demonstrates that it is not necessary for the legs toextend between two planes, so long as the legs extend between the twoplatforms. The six legs in the embodiment of FIG. 13 extend from theworkpiece platform represented by the base 180 and its columns 181, andto the spindle platform 185.

FIGS. 14-17 illustrate a ball screw driven powered leg usable with themachines of the present invention. Generally, a rotatable ball screw rod195 is mounted with a stationary platform yoke assembly indicatedgenerally by the reference numeral 196. A nut tube 197 surrounds and isoperatively connected to the ball screw rod by a plurality ofrecirculating balls 197'. The nut tube 197 is connected to a movableplatform yoke assembly indicated generally by the numeral 198. The yokeassemblies 196 and 198 are connected to the stationary and movableplatforms of the machine tool, respectively. The ball screw rod 195 isrotated by a hydraulic or electric motor 199 mounted on a bracket 200connected to the stationary yoke assembly 196. The motor has an outputshaft 201 connected to the ball screw rod 195 by a toothed belt 202operating between pulleys connectively to the output shaft 201 and theball screw rod 195. The ball screw rod 195 is journaled in a pair ofthrust bearings 203 mounted in a cage associated with a motor fork 204that forms part of the stationary platform yoke assembly 196. A bellows205 is connected at one end to the nut tube 197 and at the other end toa tube 206 which, in turn, is connected to the motor fork 204.

As the ball screw rod 195 is rotated by the motor 199, the nut tube 197will move along the length of the rod 195 in a direction dependent uponthe direction of rotation of the rod 195. The effect will be to reduceor extend the distance between the yoke assemblies 196 and 198 therebyvarying the effective length of the leg.

Referring specifically to FIGS. 15-17, the movable platform yokeassembly 198 includes a U-shaped fork 210 which is connected to the nuttube 197 and which has a central opening 211 through which the screw rod195 passes. A protective tube 212 extends from the fork 210 along theoutside of the screw rod 195. The side arms 213 and 214 of the fork 210mount bearing holders 215 that hold the inner race of thrust bearings216 which are received in recesses in opposite side faces of a block217. The block 217 has a central opening 220 which is flared from themid-point of the opening towards the opposite ends of the block 217, asshown in FIG. 16. The remaining two side faces of the block 217 havebearing recesses 221 which receive thrust bearings 222 held in place bya bearing retainers 223. The bearing retainers 223 are mounted in spacedarms 224 of a second fork attached to the movable platform. By reason ofthe construction, the two forks are disposed at 90° from each other.

As will be appreciated, the yoke assembly 198 allows rotary motion aboutan axis through the bearings 222 and rotary motion about an axis throughthe bearings 216. The flared shape of the opening 220 accommodates thelatter rotary motion. The construction and operation of the fixedplatform yoke assembly 196 is the same as that described for the movableplatform yoke assembly 198.

Mounting the yoke assemblies at points along the length of the poweredleg, rather than at the ends, results in a significant increase in theratio of the maximum to minimum distance between the yoke assemblies asthe leg moves.

A first proximity switch 225 is mounted in the nut tube 197 near thecage for the balls. A second proximity switch 226 is mounted near theend of the protective tube 212. The proximity switches 225 and 226 areused to halt motion when the ball screw rod 195 reaches the limits ofits allowed motion. That is, when the end of the ball screw rod 195changes the state of the proximity switch 226, the power leg will havebeen shortened to its pre-established limit of travel. The conditionshowing FIG. 14 is near that short limit of travel. On the other hand,when the end of the ball screw 195 changes the state of the proximityswitch 225, the length of the powered leg will have been extended to itsmaximum desired limit. In both cases, the proximity switches 225 and 226affect the continued actuation of the motor 199.

One form of instrument arm usable with the machine tools of the presentinvention, is illustrated in FIGS. 18 and 19. One end of the instrumentarm is formed with a solid rod 230 which anchors one end of a first tube231. The other end of the tube 231 mounts a slide bearing 232 whichslides about the outer one of a pair of concentric stationary tubes 233and 234. The stationary tubes 233 and 234 are each anchored on a rod 235forming the opposite end of the instrument arm. An outer protective tube236 is also anchored to the second rod 235 and surrounds the first tube231. It can be seen, therefore, that the first tube 231 can telescoperelative to the stationary tubes 233 and 234 and the protective tube236.

One end of a scale rod 238 is anchored in the solid rod end 230 of theinstrument arm. The opposite end of the scale rod 238 is attached to apiston 239 which slides within the inner stationary tube 234. A readhead 240 surrounds the scale rod and is attached to the free end of theinner and outer stationary tubes 233 and 234. The read head 240 istherefore stationary with respect to the fixed end 235 of the instrumentarm and the scale rod 238 can move longitudinally within the read head240 as the instrument arm is extended or contracted. The scale rod 238and reading head 240 are of known construction and operation. Generally,the read head will sense increments of motion along the scale rod as thetwo are moved relative to each other and will produce a signal whichwhen amplified is used in a known manner to indicate the relativeposition and changes in position of the two parts. A usable digitalpositioning measuring system of scale rod and read head may be thatbuilt by Sokki Electronics Corporation and identified as the JS7 seriesof digital positioning systems.

It is important in the operation of the read head and scale rod that thescale rod be kept taut. To that end, air pressure is introduced to actupon the piston 239 which mounts one end of the scale rod 238. The airunder pressure is introduced through a central bore 245 in the fixed end235 of the instrument arm and the air under pressure travels through thespace between the inner and outer tubes 233 and 234 and to and throughan opening 246 in the inner tube 234 adjacent its attachment to the readhead 240. This introduces pressurized air to the hollow interior of theinner tube 234 in which the position 239 rides. An orifice passageway247 extends longitudinally through the read head 240 so that the spacebetween the solid rod 230 of the instrument arm and the read head 240 isconnected to the hollow interior a vacuum is not created in that spaceas the two ends of the instrument arm move relative to each other. Thespace between the inner and outer stationary tubes 233 and 234 is alsoused to accommodate wiring 248 connecting the read head to the exteriorof the instrument arm.

The instrument arm is preferably mounted in a manner similar to that ofthe powered legs using yoke assemblies. As with the powered legs, toincrease the ratio of the maximum to minimum distance between the yokeassemblies, the yoke assemblies are preferably mounted intermediate theends such as at the locations 249 and 250 identified in FIG. 18.

The movable end 230 of the instrument arm includes a transverse casting255 having an inlet 256 and an outlet 257 for air under pressure. Theinlet and outlet are connected to a central circular raceway 258 inwhich a ball bearing 259 is disposed. Air under pressure introduced intothe casting 255 will cause the ball bearing 259 to roll rapidly alongthe raceway 258. This will induce an eccentric motion to the end 230 ofthe instrument arm about the longitudinal axis of the arm. Thiseccentric motion is useful to insure that the telescoping elements ofthe instrument arm can slide smoothly with respect to each other. At thesame time, the vibratory motion induced by the spinning ball bearing 259is in a direction transverse to the direction of motion being measuredand therefore does not significantly affect that measurement.

FIG. 20 illustrates a form of instrument arm which uses a laserinterferometer. The instrument arm is formed of concentric inner andouter tubes 260 and 261, respectively, that slide past each other onbearings 262 which preferably are made of a polytetraflouride material.A bellows 263 connects the end of the outer tube 261 to the outside ofthe inner tube 260 so as to close off the volume within the tubes andprevent contamination through the bearings 262. A laser beam from alaser light source 264 enters the hollow interior of the instrument legthrough a window 265 and is reflected off a mirror 266 into aninterferometer 267 where it is divided into two components. Onecomponent exits the interferometer and travels inside of the tubes to aretro-reflector 268 which is mounted at the closed end of the outer tube261. Light is reflected back down the tubes towards the interferometer267. The two light beam components are recombined within theinterferometer 267 and the combined components interfere with eacheither constructively or destructively depending on their phase. A photodetector within the laser source 264 detects the fringes that resultfrom the interferences between the two components of the light beam asthe retro-reflector 268 moves relative to the interferometer. The phaseis dependent upon the distance between the interferometer 267 and theretroreflector 268 and the fringes are therefore indicative of changesin length of the instrument arm.

The number of light waves in transit between the interferometer 267 andthe retro-reflector 268 depends not only on the distance between the twobut also on the speed of light. The speed of light in air is dependentupon the atmospheric pressure, temperature and humidity. Pressure andtemperature have the largest effect and therefore they must be known ifthe distance between the interferometer and retro-reflector is to becalculated based on the number of fringes. The air within the interiorof the instrument arm is vented to a collapsible bladder 270. As theinstrument arm expands, it displaces air that is stored within thebladder 270. The bladder 270 is limp at all times so that the pressurewithin the arm is equal to the ambient pressure outside of the arm. Asingle pressure transducer can then be used for all of the instrumentarms to determine the pressure of the air through which the light beamis passing.

A temperature measurement transducer 271 senses the internal temperaturein each instrument arm since the temperature may be localized. Theeffect of humidity is negligible and is ignored.

Instead of an instrument arm that has a structural integrity, it ispossible to use known forms of position transducers to measure thedistance between the platforms. An example of a usable positiontransducer is the cable actuated displacement transducers available fromHouston Scientific International, Inc. and identified as the 1850Series. In using such a transducer, a cable would be connected to one ofthe platforms and the transducer housing to the other platform. Apotentiometer within the housing would provide a signal indicative ofthe length of cable extending from the housing at any particularposition of the machine tool components.

A combination of measurements using the power legs and instrument armscan also be used to speed up positioning of the components of themachines. For example, the powered legs could be provided with a linearscale (such as in FIG. 8) or a rotary resolver or shaft encoder (such asin FIG. 9) to provide a position feedback signal that allows a grosspositioning of the platforms relative to each other. As associatedinstrument arm could then be used for fine positioning with the poweredlegs being moved at a slower rate to the final desired position.

The angles that the powered legs make with the platforms will effect thestiffness of the machine and the accuracy of the positioning of the toolrelative to the workpiece. The optimum position of the legs relative tothe platforms for achieving optimum vertical and horizontal stiffnesswould be about 35°. This assumes that each platform exhibits stiffnessalong its orthagonal axes. For achieving the best vertical andhorizontal resolutions to achieve accuracy, at nominal positions theoptimum angle of the legs relative to the platforms is about 41°.

The typical part program for a machine tool is designed to provideblocks of instruction concerning the X,Y,Z,A,B,C coordinates of the tooltip and workpiece relative to each other. Because the six legs of amachine tool in accordance with the present invention do not alignthemselves with the normal orthagonal coordinates, a method must bedeveloped to relate the normal coordinate block instructions to thelength of the six legs. The following method has been developed for thatpurpose. The steps are arranged in logic sequence form and can besummarized as follows:

I. Initializing present machine X,Y,Z,A,B,C coordinates

II. For each of six legs:

A. Initialize top and bottom pivot vector coordinates.

B. Calculate and initialize present leg length.

C. Define X,Y,Z,A,B,C home position for present leg length.

III. Set sub-block time (typically 0.02 seconds) sufficiently short toachieve desired linearity and precision of movement.

IV. For each part program:

A. For each block:

1. From the part program read machine coordinates of destination;X,Y,Z,A,B,C and feed rate

2. Using feed rate and sub-block time, compute the number of sub-blocksrequired to reach block destination.

3. For each sub-block:

(a) For each of six coordinates:

1. Present value=ending value of previous sub-block.

2. Ending value=(destination value minus present value) divided bynumber of sub-blocks remaining plus present value.

(b) Using the ending value of the six coordinates, compose a sub-blockending vector

(c) For each leg:

1. Rotate the top pivot vector to the ending angles for the currentsub-block.

2. Add a sub-block ending vector to the result.

3. Subtract the bottom pivot vector from the result.

4. Calculate the ending leg length by extracting the square root of thesum of the squares of the coordinates of the result of step (c) 3.

5. Convert the ending leg length to the nearest integral servo positioncommand count.

6. Send the position count to a servo command buffer.

7. Calculate the leg velocity required to reach new leg length in onesub-block time.

8. Convert the leg velocity to the nearest integral servo command count.

9. Send velocity count to the servo command buffer.

(d) Send sub-block start command simultaneously to all leg servos.

B A block is completed when no sub-blocks remain.

V. The task is completed when no blocks remain in the part program.

Initializing the present machine is a process which is known in themachine tool art as gridding. It establishes a home position in whichthe tip of the tool and the center of the workpiece cube are coincident.

A top pivot vector is the vector of the tool tip relative to a top pivotpoint for a particular leg. A bottom pivot vector is the vector of thecenter of the workpiece cube relative to a bottom pivot for a particularleg. The top pivot vectors remain at a fixed length but can rotatethrough the A,B,C coordinates. FIG. 21 is a vector diagram thatillustrates the relationship of a block vector and the resulting legvector which must be provided to achieve the instructed block vector. Itshould be understood that all of the vectors have three dimensions, eventhough they are illustrated in only two dimensions in FIG. 21.

Note that not only is the length of the leg vector important, the rateof movement of the legs is very important because controlling the rateof movement allows for contouring.

Although the invention has been described in relation to machine tools,it is also the usable in connection with any machine that requires thatan operator be brought into position with respect to an object. It isalso useful for a wide variety of tools other than the traditionalcutting tool.

We claim:
 1. A machine tool for locating a tool relative to a workpiece, comprising the combination of:a pair of spaced supports, the tool being located with respect to one of the supports and the workpiece being located with respect to the other of the supports; six leg members with each leg member being joined at a first point to one of the supports and being joined to the other support at a second point that is spaced along the leg member from the first point, the six leg members being arranged in circumferentially sequential pairs with the leg members of certain of the pairs crossing each other; and means for individually manipulating at least certain of the leg members to vary the position of the points of such leg members relative to each other.
 2. A machine tool in accordance with claim 1 together with control means for coordinating said manipulating means for at least some of the leg members.
 3. A machine tool in accordance with claim 1 wherein a first of said supports defines a base for the machine tool and the other support is held above the first support by the six leg members.
 4. A machine tool for locating a tool relative to a workpiece, comprising the combination of:a pair of spaced supports, the tool being located with respect to one of the supports and the workpiece being located with respect to the other of the supports; six leg members with each leg member being joined at a first point to one of the supports and being joined to the other support at a second point that is spaced along the leg member from the first point, the six leg members being arranged in circumferentially sequential pairs with the leg members of certain of the pairs crossing each other; and means for individually manipulating at least certain of the leg members to vary the position of the points of such leg members relative to each other, wherein one of said supports is suspended beneath the other support by the six leg members.
 5. A mechanism for locating an operator relative to an object, comprising the combination of:an operator support and an object support spaced from each other; six leg members with each leg member being joined at one point to one of the supports and being operatively connected to the other support at another point that is spaced along the leg member from the one point, the areas in the two supports circumscribed by the junctions of the leg members in each support being substantially the same; and means for individually manipulating at least certain of the leg members to vary the position of the points of such leg members relative to each other to thereby alter the position of the operator with respect to the object.
 6. A mechanism in accordance with claim 5 together with means for sensing the changes in positions of the points of the leg members; andcontrol means responsive to the sensing means, said control means coordinating said manipulating means.
 7. A mechanism for locating an operator relative to an object, comprising the combination of:an operator support and an object support spaced from each other; six leg members with each leg member being joined at one point to one of the supports and being operatively connected to the other support at another point that is spaced along the leg member from the one point, the areas in the two supports circumscribed by the junctions of the leg members in each support being substantially the same; means for individually manipulating at least certain of the leg members to vary the position of the points of such leg members relative to each other to thereby alter the position of the operator with respect to the object, the mechanism further including means for sensing the changes in positions of the points of the leg members; and control means responsive to the sensing means, said control means coordinating said manipulating means, wherein the six leg members are arranged in pairs with the leg members of each pair crossing each other.
 8. A machine tool for locating a tool relative to a workpiece, comprising the combination of:an upright rising from a base; a pair of spaced platforms, the tool being fixed with respect to one of the platforms and the workpiece being fixed with respect to the other of the platforms, a first of the platforms being supported on said upright; six powered extensible legs connecting the platforms and suspending the second platform from the first platform; and vibration dampening means in the support of the first platform to said upright.
 9. In a machine tool, the combination comprising:a first platform adapted to mount a tool; a second platform adapted to mount a workpiece; six linearly extensible legs each pivotably mounted adjacent one end to the first platform and each pivotably mounted adjacent the other end to the second platform, the pivot mountings in each platform circumscribing an area, and the areas in each of the two platforms being substantially the same; and means for individually varying the length of each leg to alter the position of the first platform and the tool with respect to the second platform and the workpiece.
 10. A machine tool in accordance with claim 9, wherein the pivot mountings for the legs attached to the first platform are disposed adjacent three points defining a triangle and the pivot mountings for the legs attached to the second platform are disposed adjacent three points defining a second triangle, and the two triangles and the six legs generally define edges of an octahedron.
 11. A machine tool in accordance with claim 9, wherein the pivot mountings of the legs to the platforms define the corners of a six-sided polygon in each platform.
 12. A machine tool in accordance with claim 9 wherein said tool is a cutting tool mounted in a spindle attached to the first platform, and the second platform defines a fixed base for the machine tool and mounts a workpiece support that mounts the workpiece.
 13. A machine tool in accordance with claim 9 wherein the first platform defines a fixed base for the machine, and the second platform is moved relative to the first platform.
 14. In a machine tool having a tool holder and a workpiece support, the combination of:an upright rising from a base that is fixed with respect to the workpiece support; a platform mounting the tool holder; six linearly extensible legs, three of said legs connecting the platform to the upright and three of said legs connecting the platform to the base; and means for individually varying the length of each leg to alter the position of the tool holder with respect to the workpiece support.
 15. A mechanism for locating an operator relative to an object, comprising:a pair of supports, the operator being located with respect to one of the supports and the object being located with respect to the other support; six powered and controllable extensible legs connecting the supports together in spaced relation; an actuator for each leg for individually extending and contracting the length of the leg; and a control for the leg actuators to coordinate the operation of the actuators to vary the position of the operator relative to the object, the control including sensing means for determining the length of each of the six legs, the sensing means including a plurality of extensible instrument arms connected between the supports independent of the legs and in a fixed relation to the legs so that a change in length of the legs alters the relationship between the supports which translates into changes in length of the instrument arms.
 16. A mechanism in accordance with claim 15 wherein the instrument arms each include a sensor providing a signal proportional to changes in length of said instrument arm.
 17. A mechanism for locating an operator relative to an object, comprising:a pair of supports, the operator being located with respect to one of the supports and the object being located with respect to the other support; six powered and controllable extensible legs connecting the supports together in spaced relation; an actuator for each leg for individually extending and contracting the length of the leg; a control for the leg actuators to coordinate the operation of the actuators to vary the position of the operator relative to the object, the control including sensing means for determining the length of each of the six legs, the sensing means including a plurality of extensible instrument arms connected between the supports in a fixed relation to the legs so that a change in length of the legs alters the relationship between the supports which translates into changes in length of the instrument arms; wherein the instrument arms each include a sensor providing a signal proportional to changes in length of said instrument arm, wherein each instrument arm includes two telescoping parts each joined respectively with one of said supports.
 18. A mechanism in accordance with claim 17 wherein the sensor comprises a scale rod connected to one of the telescoping parts and a read head connected to the other telescoping part to provide a digital signal of the movement of the read head along the scale rod.
 19. A mechanism in accordance with claim 17 wherein the sensor comprises a laser interferometer associated with one of the telescoping parts and a retro-reflector associated with the other part.
 20. A mechanism in accordance with claim 15 wherein there are six instrument arms with one arm associated with each powered leg.
 21. A mechanism in accordance with claim 20 wherein the six powered legs are arranged in pairs with the legs of each pair crossing each other, and the six instrument arms are arranged in pairs with the arms of each pair crossing each other.
 22. A machine tool for locating a tool relative to a workpiece, comprising:a base; a pair of spaced platforms, the tool being located with respect to one of the platforms and the workpiece being located with respect to the other of the platforms, a first of the platforms being supported by the base; six powered extensible legs connecting the second platform to the first platform; a manipulating mechanism to control the extension of at least some of the extensible legs; and a vibration isolation device cooperating with the base and the first of the platforms to alleviate detrimental vibration.
 23. The machine tool of claim 22, wherein the vibration isolation device includes a resilient member disposed intermediate the base and the first of the platforms.
 24. In a machine tool having a tool holder and a workpiece support, the combination comprising:a tool holder platform locating the tool holder; a workpiece support platform locating the workpiece support; six powered and controlled extensible legs connecting the platforms together in spaced relation, each of the legs being joined to the workpiece support platform at one point along the length of the leg and being joined to the tool holder platform at a second spaced point along the length of the leg; an actuator for each leg for individually extending and contracting the length of the leg; and a control for the leg actuators to coordinate the operation of the actuators to vary the position of the tool holder relative to the workpiece support, said control including sensing means for determining the length of each of the six legs, the sensing means including a plurality of extensible instrument arms connected between said platforms in a known relation to the legs so that a change in length of the legs alters the relationship between the platforms which translates into changes in length of the instrument arms, wherein each powered leg includes two telescoping parts, one of which is joined to the tool holder platform and the other of which is joined to the workpiece support platform.
 25. A machine tool in accordance with claim 24 together with means preventing the two telescoping parts from rotating with respect to each other, one of the connections of each leg to a platform having three degrees of freedom of motion and the other connection of the leg to the other platform having two degrees of freedom of motion.
 26. A mechanism for joining spaced platforms, comprising:six legs connecting the platforms together, each of the legs being joined at one point to one of the platforms and being operatively connected to the other platform at another point that is spaced from the one point; the six legs being arranged in circumferentially sequential pairs with the legs of each pair crossing each other; and a manipulator mechanism configured to manipulate at least certain of the legs to vary the positions of the points of such legs relative to each other to thereby alter the position of the platforms with respect to each other.
 27. A mechanism for locating an operator relative to an object, comprising:a pair of spaced supports, the operator being located with respect to one of the supports and the object being located with respect to the other support; and six extensible legs joining the supports, each leg comprising a ball screw rod and a nut tube surrounding the rod and joined thereto by recirculating balls, a first yoke assembly mounted with the ball screw rod to connect the leg to a first of said supports, and a second yoke assembly mounted to the nut tube to connect the leg to the second of said supports, and a motor connected to rotate said ball screw rod.
 28. A mechanism in accordance with claim 27 wherein each yoke assembly includes a pair of forks rotatably attached to side faces of a support cube, one of the forks being connected to a respective support and the other fork being connected to the leg, said cube having a central opening to receive the screw rod.
 29. A mechanism in accordance with claim 27, together with a protective tube surrounding said ball screw rod and proximity switches on said protective tube and nut tube to provide a signal when the ball screw rod has reached the limits of acceptable motion with respect to the nut tube.
 30. A method of locating an operator relative to an object, comprising the steps of:fixing the operator relative to a first support; mounting the object relative to a second support; connecting the supports together by six leg members each being joined at one point along its length to one of the supports and being operatively connected to the other support at a point that is spaced along the leg member from the one point; locating the junctions of the leg members with the supports such that the areas circumscribed by the junctions in each of the two supports is substantially the same; and manipulating the leg members to vary the position of the points of such leg members relative to each other to thereby provide three linear degrees of motion and three rotational degrees of motion, or any combination thereof, to the operator relative to the object.
 31. A mechanism for locating an operator relative to an object, comprising the combination of:a pair of supports spaced from each other, the operator being located with respect to one of the supports and the object being located with respect to the other of the supports; six leg members with each leg member being joined at one point to one of the supports and being operatively connected to the other support at another point that is spaced along the leg member from the one point, the six leg members being arranged in adjacent pairs with the leg members of certain of the pairs crossing each other; and a manipulator mechanism configured to manipulate at least certain of the leg members to vary the position of the points of such leg members relative to each other to thereby alter the position of the operator with respect to the object. 